Conversion Rules for Weyl Points and Nodal Lines in Topological Media

Area of Science:

• Condensed matter physics
• Topological materials science

Background:

• A common understanding suggests Weyl points with opposite chirality annihilate upon collision.
• This paradigm has guided research in topological phases of matter.

Purpose of the Study:

• To investigate the annihilation dynamics of Weyl points under specific symmetry constraints.
• To explore the emergence of new topological phases and surface states.

Main Methods:

• Analysis of topological crystalline invariants derived from relative homotopy theory.
• Investigation of symmetry properties, including mirror symmetry and combined symmetries (e.g., π rotation with time reversal).
• Testing predictions using simple tight-binding models.

Main Results:

• Weyl points related by mirror symmetry do not annihilate but transform into nodal loops.
• Discovery of new nodal-line and nodal-chain semimetals with Fermi-arc and drumhead surface states.
• Introduction of 'helicity' as a topological charge for Weyl points under combined symmetries, governing annihilation.

Conclusions:

• The annihilation of Weyl points is symmetry-dependent, with mirror symmetry forbidding it and leading to nodal loop formation.
• Symmetry-based topological invariants provide a powerful framework for discovering novel topological materials.
• The findings expand the understanding of topological phases and their surface phenomena.